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Picard modular surface is a complex algebraic surface obtained as an arithmetic quotient of the two-dimensional complex unit ball by a Picard modular
Picard_modular_surface
L of signature (2, 1). Picard modular groups act on the unit sphere in C2 and the quotient is called a Picard modular surface. Fuchsian group Kleinian
Picard_modular_group
French mathematician (1856–1941)
Picard. Vol. I–IV. Paris: Centre National de la Recherche Scientifique. OCLC 4615520. Émile Picard Medal Picard modular group Picard modular surface Picard
Émile_Picard
Algebraic surface in mathematics
In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies
Hilbert_modular_variety
Humbert surfaces Picard modular surfaces Shioda modular surfaces Elliptic surfaces, surfaces with an elliptic fibration; quasielliptic surfaces constitute
List of complex and algebraic surfaces
List_of_complex_and_algebraic_surfaces
Theorem in abstract algebra
Robert P.; Ramakrishnan, Dinakar (eds.), The zeta functions of Picard modular surfaces, Montreal, QC: Univ. Montréal, pp. 363–394, ISBN 978-2-921120-08-1
Fundamental lemma (Langlands program)
Fundamental_lemma_(Langlands_program)
Mathematical equation
is the upper half-plane and Γ {\displaystyle \Gamma } is the modular group. The Picard–Fuchs equation is then d 2 y d j 2 + 1 j d y d j + 31 j − 4 144
Picard–Fuchs_equation
Theorem about the range of an analytic function
plane minus a single point. Sketch of Proof: Picard's original proof was based on properties of the modular lambda function, usually denoted by λ {\textstyle
Picard_theorem
One-dimensional complex manifold
classification is reflected in maps between Riemann surfaces, as detailed in Liouville's theorem and the Little Picard theorem: maps from hyperbolic to parabolic
Riemann_surface
Mathematical concept
Macbeath surface (genus 7) First Hurwitz triplet (genus 14) and by the Fermat curve of degree 7. Other examples of Shimura varieties include Picard modular surfaces
Shimura_variety
Mathematical classification of surfaces
the dimension of the Picard variety and the Albanese variety and denoted by q. For complex surfaces (but not always for surfaces of prime characteristic)
Enriques–Kodaira classification
Enriques–Kodaira_classification
irregularity of an algebraic surface is sometimes defined to be this Hodge number, and sometimes defined to be the dimension of the Picard variety, which is the
Irregularity_of_a_surface
points on a Shimura variety modulo a prime of good reduction in The zeta functions of Picard modular surfaces, Publications du CRM, 1992, pp. 151-253.
Hyperspecial_subgroup
Mathematical surface
elliptic modular surface of level 4 (the universal generalized elliptic curve E(4) → X(4)) in characteristic 3 mod 4 is a K3 surface with Picard number
Supersingular_K3_surface
Modular function in mathematics
C to the complex plane. As a Riemann surface, the fundamental region has genus 0, and every (level one) modular function is a rational function in j;
J-invariant
Mathematical concept
elliptic fibration over the projective line. Kodaira surfaces Dolgachev surfaces Shioda modular surfaces Most of the fibers of an elliptic fibration are (non-singular)
Elliptic_surface
American mathematician (born 1937)
further into the relative theory, in defining "modular families" of curves via Grothendieck topologies, in Picard Groups of Moduli Problems. The lacuna of the
David_Mumford
class Serre's multiplicity conjectures Albanese variety Picard group Modular form Moduli space Modular equation J-invariant Algebraic function Algebraic form
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Discrete subgroup of the real projective special linear group of dimension 2
important; the so-called Picard group PSL(2,Z[i]) is discrete but does not preserve any disk in the Riemann sphere. Indeed, even the modular group PSL(2,Z), which
Fuchsian_group
17th-century conjecture proved by Andrew Wiles in 1994
known as the modularity theorem, and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques
Fermat's_Last_Theorem
Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor
(link) Fogarty, John (1973), "Algebraic families on an algebraic surface. II. The Picard scheme of the punctual Hilbert scheme", American Journal of Mathematics
Hilbert_scheme
areas of research include: Complex analysis: automorphic functions and modular forms Arithmetic: algebraic number theory, algorithmic algebra, and arithmetical
Heidelberg University Faculty of Mathematics and Computer Science
Heidelberg_University_Faculty_of_Mathematics_and_Computer_Science
Belgian mathematician (born 1944)
with Ken Ribet on abelian L-functions and their extensions to Hilbert modular surfaces and p-adic L-functions form an important part of his work in arithmetic
Pierre_Deligne
d'existence en géométrie algébrique. V : Les schémas de Picard : Théorèmes d'existence (Picard schemes) Bernard Morin, Champs de vecteurs sur les sphères
Séminaire Nicolas Bourbaki (1960–1969)
Séminaire_Nicolas_Bourbaki_(1960–1969)
Type of group in group theory
with unitary groups of hermitian forms, a well-known example is the Picard modular group. When G {\displaystyle G} is a Lie group one can define an arithmetic
Arithmetic_group
Counterintuitive mathematical object
(written with Enrico Bombieri). It can be explained in terms of the Picard scheme of the surface, and in particular, its failure to be a reduced scheme, a theme
Pathological_(mathematics)
Algebraic curve in mathematics
algebra systems Elliptic algebra Elliptic surface Isogeny j-line Level structure (algebraic geometry) Modularity theorem Moduli stack of elliptic curves
Elliptic_curve
Mathematical object studied in the field of algebraic geometry
associated to the graded ring formed by modular forms (in the Siegel case, Siegel modular forms; see also Siegel modular variety). The non-uniqueness of compactifications
Algebraic_variety
Study of complex manifolds and several complex variables
is given by the Picard variety Pic(X) of X. The picard variety can be easily described in the case where X is a compact Riemann surface of genus g. Namely
Complex_geometry
Conformal mappings in complex analysis
function for that triangle's triangle group. More specifically, it is a modular function. Let πα, πβ, and πγ be the interior angles at the vertices of
Schwarz_triangle_function
Functions c.1910 The theory of Poincaré normal functions implies that the Picard variety and Albanese variety are isogenous. 1913 Torelli's theorem 1916
Timeline_of_abelian_varieties
Geometric space whose points represent algebro-geometric objects of some fixed kind
stack of elliptic curves Moduli spaces of K-stable Fano varieties Modular curve Picard functor Moduli of semistable sheaves on a curve Seiberg–Witten moduli
Moduli_space
"Marvel's 'Vision Quest' Recasts a Major MCU Character With a 'Star Trek: Picard' Fan-Favorite". Collider. Archived from the original on August 9, 2025.
Features of the Marvel Cinematic Universe
Features_of_the_Marvel_Cinematic_Universe
Technology development overview
spacecraft Satellites and space stations International Space Station – Modular space station in low Earth orbit Mir – Soviet/Russian space station (1986–2001)
Outline of artificial satellites
Outline_of_artificial_satellites
Projective variety that is also an algebraic group
appear naturally as Jacobian varieties (the connected components of zero in Picard varieties) and Albanese varieties of other algebraic varieties. The group
Abelian_variety
Zariski-open subset U is proportional to Blog(B)r−1, where r is rank of Picard group of that variety. Sato–Tate conjecture: also a number of related conjectures
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Infantry]. Thai Army (in Thai). Archived from the original on 24 March 2019. Picard, Michael; Holtom, Paul; Mangan, Fiona (December 2019). "Trade Update 2019:
List of equipment of the Royal Thai Army
List_of_equipment_of_the_Royal_Thai_Army
Temple on the Athenian Acropolis, Greece
Hellmann, L'Architecture grecque. Architecture religieuse et funéraire, Picard, 2006, p. 118. B. Nagy, "Athenian Officials on the Parthenon Frieze", AJA
Parthenon
Protein found in humans
{{cite book}}: CS1 maint: location missing publisher (link) von Bernuth H, Picard C, Jin Z, Pankla R, Xiao H, Ku CL, et al. (August 2008). "Pyogenic bacterial
MYD88
logic instead of classical logic. Partition theory Perturbation theory Picard–Vessiot theory Plane geometry Point-set topology see general topology Pointless
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Lacking stable, safe, functional housing
August 2009. Retrieved 7 September 2006. Collet Marc, Menahem, Georges, Picard, Hervé, "Why patients attending free health centres seek care: Precalog
Homelessness
encyclopedia for computers (The Electronic Encyclopedia). Pioneered a modular PBX communication system integrating land-lines with mobile phones (Intelliphone)
List of pioneers in computer science
List_of_pioneers_in_computer_science
French mathematician (1928–2014)
Science & Business Media. pp. 156–. ISBN 978-81-322-0769-6. R. P. Langlands, Modular forms and l-adic representations, Lecture Notes in Math. 349. (1973), 361—500
Alexander_Grothendieck
Hecke, I (modular forms) Jacques-Louis Lions, Les travaux de Deny en théorie du potentiel (potential theory) Pierre Samuel, Variété de Picard et groupe
Séminaire Nicolas Bourbaki (1950–1959)
Séminaire_Nicolas_Bourbaki_(1950–1959)
Prefecture and commune in Bourgogne-Franche-Comté, France
artificial cave, a Wallace fountain, statues of Victor Hugo and Auguste Veil-Picard, the portal of the church of the convent of the Great Carmelites, and a
Besançon
theorem (complex analysis) Phragmén–Lindelöf theorem (complex analysis) Picard theorem (complex analysis) Residue theorem (complex analysis) Riemann mapping
List_of_theorems
theorist Ling Long (mathematician), Chinese-American expert on modular forms, elliptic surfaces, and dessins d'enfants Lynette Long, American psychologist
List_of_women_in_mathematics
Encyclopedia Britannica. Retrieved 13 June 2019. "Picard". nssdc.gsfc.nasa.gov. Retrieved 13 June 2019. "Picard". Picard. 24 April 2015. Retrieved 13 June 2019.
Timeline of Solar System exploration
Timeline_of_Solar_System_exploration
American artist
work with that of sixteen artists who influenced her. Artforum's Caroline Picard called it "a profound conversation between objects and aesthetic experiments
Jessica_Stockholder
On generating functions from counting points on algebraic varieties over finite fields
Margulis shows that the image of the monodromy group acting on E, given by the Picard–Lefschetz formula, is Zariski dense in a symplectic group and therefore
Weil_conjectures
Generalization of algebraic spaces or schemes
_{n}} -torsors is representable as a stack over the Etale topology, but the Picard-stack B G m {\displaystyle B\mathbb {G} _{m}} of G m {\displaystyle \mathbb
Algebraic_stack
were displayed solely for the use of students and teachers, until Maurice Picard, a Jewish French watch-making industrialist gave impetus to the idea of
International Museum of Horology
International_Museum_of_Horology
Algebraic structure
flat connection is a Gauss–Manin connection ∇ and can be described by the Picard–Fuchs equation. A variation of mixed Hodge structure can be defined in a
Hodge_structure
of rails belonging to the genus Dryolimnas from the Pleistocene of the Picard Island (Seychelles) is published by Hume & Martill (2019), who interpret
2019 in archosaur paleontology
2019_in_archosaur_paleontology
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